Two events are independent if the probability of one event occurring is not affected by the occurrence of the other event.

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## Introduction

events are two events that have no influence on each other. That is, the occurrence of event A does not affect the probability of event B occurring and vice versa.

For example, imagine you’re flipping a coin. The probability of flipping a tails is 50% on any given flip, regardless of whether the previous flip was tails or heads. In other words, the flips are independent of each other.

Another example where events are dependent would be if you’re pulling cards from a deck. After every card is pulled, the probability of the next card being an ace changes. For example, say there’s only one ace in a deck of 52 cards. The probability of the first card being an ace is 1/52 or 2%. But after the first card is pulled (let’s say it’s not an ace), the probability becomes 3/51 or 5.88%.

## What are independent events?

An independent event is an event that is not affected by any other events. In other words, the outcome of one event does not affect the outcome of another event. For example, if you flip a coin, the outcome of that event (heads or tails) does not affect the outcome of the next coin flip.

### Two events are independent if the occurrence of one does not affect the probability of the other.

Two events are independent if the occurrence of one does not affect the probability of the other. This means that the two events are not related in any way.

For example, let’s say you’re flipping a coin. The probability of getting heads is 50%. If you flip the coin again, the probability of getting heads is still 50%. The two events (getting heads on the first flip and getting heads on the second flip) are independent because the first event has no bearing on the second event.

Another example of independence is rolling a die. The probability of rolling a 6 is 1/6. If you roll the die again, the probability of rolling a 6 is still 1/6. The two events (rolling a 6 on the first roll and rolling a 6 on the second roll) are independent because the first event has no bearing on

the second event.

### Probability of the two events occurring together = Probability of event 1 x Probability of event 2

The probability of two events occurring together is calculated by multiplying the probability of one event by the probability of the other event. This is only true if the events are independent, meaning that the occurrence of one event does not affect the probability of the other event occurring.

For example, if you flip a coin and then roll a die, the two events are independent because whether the coin comes up heads or tails does not affect whether the die comes up 1, 2, 3, 4, 5, or 6. The probability of both events occurring together is 0.5 (the probability of heads) x 0.1666 (the probability of 1), which equals 0.0833.

## Examples of independent events

Two events are said to be independent if the occurrence of one doesn’t affect the probability of the other. For example, the weather conditions on two separate days are independent events. Here are some more examples of independent events.

### Rolling two dice

If you roll two dice, the outcome of the first roll doesn’t affect the outcome of the second roll. So, rolling a 1 on the first die and a 2 on the second die is just as likely as rolling a 2 on the first die and a 1 on the second die.

Here’s another way to think about it. If you roll two dice, each die has a 1/6 chance of landing on any given number. So, the chance of rolling a 1 on the first die and a 2 on the second die is (1/6 x 1/6), which is also the chance of rolling a 2 on the first die and a 1 on the second die.

### Drawing two cards from a deck

Here’s an example of two events that are independent: drawing two cards from a deck. It doesn’t matter what the first card is; it doesn’t affect the probability of drawing a specific second card. So, if you’re looking for a specific pair of cards, the probability is the same as if you were drawing just one card. The probability of drawing any Ace is 4/52 (1/13), so the probability of drawing an Ace and then a 2 would be (4/52) x (4/52), or 1/169.

## Why are independent events important?

Two events are said to be independent if the occurrence of one doesn’t affect the probability of the other. In other words, the events are not related. It’s important to know if events are independent because it helps us calculate probabilities. If events are not independent, then we have to account for the dependency when calculating probabilities.

### They allow us to calculate the probability of multiple events occurring

Independent events are important because they allow us to calculate the probability of multiple events occurring. Probability is the chance that something will happen, and it is affected by how likely the event is to occur and how many chances there are for it to occur.

Independent events are important because they allow us to calculate the probability of multiple events occurring. Probability is the chance that something will happen, and it is affected by how likely the event is to occur and how many chances there are for it to occur.

For example, if you flip a coin, the probability of it landing on heads is 50%. If you flip the coin again, the probability of it landing on heads is still 50%. But if you flip the coin twice, the probability of both flips landing on heads is 25% (50% x 50%).

The reason for this decrease is because each time you flip the coin, there are fewer chances for heads to come up. This happens because each time you flip the coin, there are two possible outcomes (heads or tails), and each outcome affects the probability of the next outcome. So, in order for two heads to come up in a row, both flips would have to land on heads, which is less likely than just one head coming up.

This same principle can be applied to other independent events, like rolling dice or drawing cards from a deck. The more times you perform an independent event, the less likely it becomes that all of those events will have the same outcome.

### They are the basis for the multiplication rule

Independent events are important because they are the basis for the multiplication rule. The multiplication rule states that if two events are independent, then the probability of both events occurring is the product of the probabilities of each event occurring. For example, if the probability of event A is 0.5 and the probability of event B is 0.3, then the probability of both events occurring is 0.5 x 0.3 = 0.15.

The multiplication rule is important because it allows us to calculate the probability of more than one event occurring. For example, if we want to know the probability of rolling a 5 on a dice and flipping a coin landing on heads, we can use the multiplication rule to calculate this. We know that the probability of rolling a 5 on a dice is 1/6 (there are 6 possible outcomes when rolling a dice and 1 of those is rolling a 5) and we also know that the probability of flipping a coin and landing on heads is 1/2 (there are 2 possible outcomes when flipping a coin – heads or tails, and 1 of those is heads). So using the multiplication rule we can calculate that the probability of rolling a 5 on a dice AND flipping a coin and landing on heads is 1/6 x 1/2 = 1/12.

## Conclusion

Now you know that independent events are those which occur without influence from each other. Dependent events, on the other hand, are partially or wholly influenced by other events. You also know that you can use a couple of different formulas to find the probability of two events occurring together.